The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=-3\) and \(k=-4\).
To get the correct daughter graph, translate the parent 3 units left and 4 units down. Since \(a>0\), the daughter points up.
The correct plot is Plot 3.
\[y = \left|{x + 3}\right| - 4\]
Question
Which plot matches the function:
\[y = 4 - \left|{x + 2}\right|\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=-2\) and \(k=4\).
To get the correct daughter graph, translate the parent 2 units left and 4 units up. Since \(a<0\), the daughter points down.
The correct plot is Plot 4.
\[y = 4 - \left|{x + 2}\right|\]
Question
Which plot matches the function:
\[y = - \left|{x + 5}\right| - 1\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=-5\) and \(k=-1\).
To get the correct daughter graph, translate the parent 5 units left and 1 units down. Since \(a<0\), the daughter points down.
The correct plot is Plot 3.
\[y = - \left|{x + 5}\right| - 1\]
Question
Which plot matches the function:
\[y = \left|{x + 4}\right| - 5\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=-4\) and \(k=-5\).
To get the correct daughter graph, translate the parent 4 units left and 5 units down. Since \(a>0\), the daughter points up.
The correct plot is Plot 4.
\[y = \left|{x + 4}\right| - 5\]
Question
Which plot matches the function:
\[y = \left|{x + 5}\right| - 6\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=-5\) and \(k=-6\).
To get the correct daughter graph, translate the parent 5 units left and 6 units down. Since \(a>0\), the daughter points up.
The correct plot is Plot 1.
\[y = \left|{x + 5}\right| - 6\]
Question
Which plot matches the function:
\[y = - \left|{x + 4}\right| - 6\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=-4\) and \(k=-6\).
To get the correct daughter graph, translate the parent 4 units left and 6 units down. Since \(a<0\), the daughter points down.
The correct plot is Plot 1.
\[y = - \left|{x + 4}\right| - 6\]
Question
Which plot matches the function:
\[y = - \left|{x - 2}\right| - 4\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=2\) and \(k=-4\).
To get the correct daughter graph, translate the parent 2 units right and 4 units down. Since \(a<0\), the daughter points down.
The correct plot is Plot 3.
\[y = - \left|{x - 2}\right| - 4\]
Question
Which plot matches the function:
\[y = 6 - \left|{x + 1}\right|\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=-1\) and \(k=6\).
To get the correct daughter graph, translate the parent 1 units left and 6 units up. Since \(a<0\), the daughter points down.
The correct plot is Plot 3.
\[y = 6 - \left|{x + 1}\right|\]
Question
Which plot matches the function:
\[y = 2 - \left|{x + 6}\right|\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=-6\) and \(k=2\).
To get the correct daughter graph, translate the parent 6 units left and 2 units up. Since \(a<0\), the daughter points down.
The correct plot is Plot 2.
\[y = 2 - \left|{x + 6}\right|\]
Question
Which plot matches the function:
\[y = \left|{x - 6}\right| + 4\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=6\) and \(k=4\).
To get the correct daughter graph, translate the parent 6 units right and 4 units up. Since \(a>0\), the daughter points up.
The correct plot is Plot 3.
\[y = \left|{x - 6}\right| + 4\]
Question
Which plot matches the function:
\[y = - \left|{x + 5}\right| - 2\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=-5\) and \(k=-2\).
To get the correct daughter graph, translate the parent 5 units left and 2 units down. Since \(a<0\), the daughter points down.
The correct plot is Plot 4.
\[y = - \left|{x + 5}\right| - 2\]
Question
Which plot matches the function:
\[y = \left|{x + 3}\right| + 2\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=-3\) and \(k=2\).
To get the correct daughter graph, translate the parent 3 units left and 2 units up. Since \(a>0\), the daughter points up.
The correct plot is Plot 2.
\[y = \left|{x + 3}\right| + 2\]
Question
Which plot matches the function:
\[y = \left|{x + 3}\right| - 2\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=-3\) and \(k=-2\).
To get the correct daughter graph, translate the parent 3 units left and 2 units down. Since \(a>0\), the daughter points up.
The correct plot is Plot 4.
\[y = \left|{x + 3}\right| - 2\]
Question
Which plot matches the function:
\[y = - \left|{x - 2}\right| - 6\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=2\) and \(k=-6\).
To get the correct daughter graph, translate the parent 2 units right and 6 units down. Since \(a<0\), the daughter points down.
The correct plot is Plot 3.
\[y = - \left|{x - 2}\right| - 6\]
Question
Which plot matches the function:
\[y = 1 - \left|{x + 2}\right|\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=-2\) and \(k=1\).
To get the correct daughter graph, translate the parent 2 units left and 1 units up. Since \(a<0\), the daughter points down.
The correct plot is Plot 4.
\[y = 1 - \left|{x + 2}\right|\]
Question
Which plot matches the function:
\[y = \left|{x + 6}\right| - 5\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=-6\) and \(k=-5\).
To get the correct daughter graph, translate the parent 6 units left and 5 units down. Since \(a>0\), the daughter points up.
The correct plot is Plot 4.
\[y = \left|{x + 6}\right| - 5\]
Question
Which plot matches the function:
\[y = - \left|{x - 3}\right| - 2\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=3\) and \(k=-2\).
To get the correct daughter graph, translate the parent 3 units right and 2 units down. Since \(a<0\), the daughter points down.
The correct plot is Plot 3.
\[y = - \left|{x - 3}\right| - 2\]
Question
Which plot matches the function:
\[y = 1 - \left|{x - 4}\right|\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=4\) and \(k=1\).
To get the correct daughter graph, translate the parent 4 units right and 1 units up. Since \(a<0\), the daughter points down.
The correct plot is Plot 3.
\[y = 1 - \left|{x - 4}\right|\]
Question
Which plot matches the function:
\[y = \left|{x + 1}\right| + 2\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=-1\) and \(k=2\).
To get the correct daughter graph, translate the parent 1 units left and 2 units up. Since \(a>0\), the daughter points up.
The correct plot is Plot 4.
\[y = \left|{x + 1}\right| + 2\]
Question
Which plot matches the function:
\[y = \left|{x - 1}\right| + 5\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(y=|x|\), which has a vertex at the origin.
The general parameterization is \(y=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=1\) and \(k=5\).
To get the correct daughter graph, translate the parent 1 units right and 5 units up. Since \(a>0\), the daughter points up.
